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\begin{figure}\centerline{ \psfig{file=problems/prob_5_5.eps,height=2.5in} }\end{figure}

In the circuit above, assume $R$, $C$, and $V$ are given. Derive all your answers for up to five bonus points, but you may just give the answers below for full credit. All answers may be expressed in terms of powers of $e$.

a) At time $t = 0$, switch 1 is closed. What is the charge on the capacitor as a function of time in terms of the given quantities.

b) After a very long time ($\gg RC$) switch 1 is opened and switch 2 is closed. What is the voltage across the capacitor as a function of time.

c) At time $t = 2RC$ switch 2 is opened. How much energy is stored in the capacitor at that time?

Robert G. Brown 2003-02-09